Structure preserving reduced order modeling for gradient systems

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dc.authoridUzunca, Murat/0000-0001-5262-063X
dc.authoridAkman, Tugba/0000-0003-1206-2287
dc.contributor.authorAkman Yildiz, Tugba
dc.contributor.authorUzunca, Murat
dc.contributor.authorKarasozen, Bulent
dc.date.accessioned2025-03-23T19:42:10Z
dc.date.available2025-03-23T19:42:10Z
dc.date.issued2019
dc.departmentSinop Üniversitesi
dc.description.abstractMinimization of energy in gradient systems leads to formation of oscillatory and Turing patterns in reaction-diffusion systems. These patterns should be accurately computed using fine space and time meshes over long time horizons to reach the spatially inhomogeneous steady state. In this paper, a reduced order model (ROM) is developed which preserves the gradient dissipative structure. The coupled system of reaction-diffusion equations are discretized in space by the symmetric interior penalty discontinuous Galerkin (SIPG) method. The resulting system of ordinary differential equations (ODEs) are integrated in time by the average vector field (AVF) method, which preserves the energy dissipation of the gradient systems. The ROMs are constructed by the proper orthogonal decomposition (POD) with Galerkin projection. The nonlinear reaction terms are computed efficiently by discrete empirical interpolation method (DEIM). Preservation of the discrete energy of the FOMs and ROMs with POD-DEIM ensures the long term stability of the steady state solutions. Numerical simulations are performed for the gradient dissipative systems with two specific equations; real Ginzburg-Landau equation and Swift-Hohenberg equation. Numerical results demonstrate that the POD-DEIM reduced order solutions preserve well the energy dissipation over time and at the steady state. (C) 2018 Elsevier Inc. All rights reserved.
dc.identifier.doi10.1016/j.amc.2018.11.008
dc.identifier.endpage209
dc.identifier.issn0096-3003
dc.identifier.issn1873-5649
dc.identifier.scopus2-s2.0-85056852432
dc.identifier.scopusqualityQ1
dc.identifier.startpage194
dc.identifier.urihttps://doi.org/10.1016/j.amc.2018.11.008
dc.identifier.urihttps://hdl.handle.net/11486/6718
dc.identifier.volume347
dc.identifier.wosWOS:000454116700016
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherElsevier Science Inc
dc.relation.ispartofApplied Mathematics and Computation
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WOS_20250323
dc.subjectGradient systems
dc.subjectPattern formation
dc.subjectDiscontinuous Galerkin method
dc.subjectAverage vector field method
dc.subjectProper orthogonal decomposition
dc.subjectDiscrete empirical interpolation
dc.titleStructure preserving reduced order modeling for gradient systems
dc.typeArticle

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